MCMC algorithms for supervised and unsupervised linear unmixing of hyperspectral images

International audienceIn this paper, we describe two fully Bayesian algorithms that have been previously proposed to unmix hyperspectral images. These algorithms relies on the widely admitted linear mixing model, i.e. each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra. First, the unmixing problem is addressed in a supervised framework, i.e., when the endmembers are perfectly known, or previously identified by an endmember extraction algorithm. In such scenario, the unmixing problem consists of estimating the mixing coefficients under positivity and additivity constraints. Then the previous algorithm is extended to handle the unsupervised unmixing problem, i.e., to estimate the endmembers and the mixing coefficients jointly. This blind source separation problem is solved in a lower-dimensional space, which effectively reduces the number of degrees of freedom of the unknown parameters. For both scenarios, appropriate distributions are assigned to the unknown parameters, that are estimated from their posterior distribution. Markov chain Monte Carlo (MCMC) algorithms are then developed to approximate the Bayesian estimators

How the optical properties of leaves modify the absorption and scattering of energy and enhance leaf functionality

International audienceLeaves absorb, scatter, and transmit sunlight at all wavelengths across the visible, near-infrared, and shortwave-infrared spectrum. The optical properties of a leaf are determined by its biochemical and biophysical characteristics, including its 3-D cellular organization. The absorption and scattering properties of leaves together create the shape of their reflectance spectra. Terrestrial seed plant species share similar physiological and metabolic processes for fluxes of gases (CO2, O2, H2O), nutrients, and energy, while differences are primarily consequences of how these properties are distributed and their physical structures. Related species generally share biochemical and biophysical traits, and their optical properties are also similar, providing a mechanism for identification. However, it is often the minor differences in spectral properties throughout the wavelengths of the solar spectrum that define a species or groups of related species. This chapter provides a review and summary of the most common interactions between leaf properties and light and the physical processes that regulate the outcomes of these interactions